1 Answer
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In this usage that introduces a defining clause, i.e. one that modifies and restricts the meaning of the immediately preceding noun. Because a that clause is essential (critical) in defining and restricting the noun, it is NOT normally preceded by a comma.

Which is generally used to introduce a descriptive clause, i.e. one that adds additional information, but is not essential to the meaning of the sentence. Being optional - rather than essential - to the sentence, a which clause IS normally preceded by a comma.

Which clauses are sometimes used as defining clauses, in the same way as that clauses, in which case they should NOT be preceded by a comma.

I find the sentence in question somewhat ambiguous:

Iraq ... [is now] ... being reconstructed by the U.S. corporations, which were the cause of its deliberate destruction.

because of the highlighted word the.

If you omit that word:

... being reconstructed by U.S. corporations, which were the cause of its deliberate destruction.

I read it as meaning that it is

... being reconstructed by U.S. corporations [in general], [some of] which were the cause of its deliberate destruction.

But with the U.S. corporations, it invites the following clause to define which particular U.S. corporations are being referred to - in other words, it requires a defining clause. In that case, that or which - but without the preceding comma - would be appropriate:

... being reconstructed by the U.S. corporations that were the cause of its deliberate destruction.

Grammatically, that makes sense and would be correct, but I doubt that the sentence is actually intended to mean that the reconstruction is being carried out either solely by nor by all of those particular U.S. corporations that were the cause of its deliberate destruction.

So my answer would be that the quoted sentence is actually ambiguous, but I suspect that the intended meaning is:

Iraq ... [is now] ... being reconstructed by U.S. corporations, some of which were the cause of its deliberate destruction.

rather than:

Iraq ... [is now] ... being reconstructed by the [i.e. those particular] U.S. corporations that were the cause of its deliberate destruction.